Question: Divide the following complex numbers: $\dfrac{6(\cos(\frac{5}{4}\pi) + i \sin(\frac{5}{4}\pi))}{\cos(\frac{13}{12}\pi) + i \sin(\frac{13}{12}\pi)}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $6(\cos(\frac{5}{4}\pi) + i \sin(\frac{5}{4}\pi))$ ) has angle $\frac{5}{4}\pi$ and radius 6. The second number ( $\cos(\frac{13}{12}\pi) + i \sin(\frac{13}{12}\pi)$ ) has angle $\frac{13}{12}\pi$ and radius 1. The radius of the result will be $\frac{6}{1}$ , which is 6. The angle of the result is $\frac{5}{4}\pi - \frac{13}{12}\pi = \frac{1}{6}\pi$ The radius of the result is $6$ and the angle of the result is $\frac{1}{6}\pi$.